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Paul George

Numerade Educator

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Numerade tutor for 7 years
37 Students Helped

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Unlocking the Power of Functions: Boost Your Programming Skills
Breaking Limits: Unlock Your Potential with Our Expert Solutions

Paul's Textbook Answer Videos

02:40
Biocalculus Calculus for the Life Sciences

Explain what it means to say that
$\lim _{x \rightarrow 1^{-}} f(x)=3 \quad$ and $\quad \lim _{x \rightarrow 1^{+}} f(x)=7$
In this situation is it possible that $\lim _{x \rightarrow 1} f(x)$ exists? Explain.

Chapter 2: Limits
Section 3: Limits of Functions at Finite Numbers
Paul George
02:52
Biocalculus Calculus for the Life Sciences

Use the given graph of $f$ to state the value of each quantity, if it exists. If it does not exist, explain why.
$$ \begin{array}{ll}{\text { (a) } \lim _{x \rightarrow 2^{-}} f(x)} & {\text { (b) } \lim _{x \rightarrow 2^{+}} f(x)} & {\text { (c) } \lim _{x \rightarrow 2} f(x)} \\ {\text { (d) } f(2)} & {\text { (e) } \lim _{x \rightarrow 4} f(x)} & {\text { (f) } f(4)}\end{array} $$

Chapter 2: Limits
Section 3: Limits of Functions at Finite Numbers
Paul George
07:58
Biocalculus Calculus for the Life Sciences

For the function $f$ whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.
(a) $\lim _{x \rightarrow-3^{-}} h(x) \quad$
(b) $\lim _{x \rightarrow-3^{+}} h(x) \quad$
(c) $\lim _{x \rightarrow-3} h(x)$
(d) $h(-3) \quad$
(e) $\lim _{x \rightarrow 0^{-}} h(x) \quad$
(f) $\lim _{x \rightarrow 0^{+}} h(x)$
(g) $\lim _{x \rightarrow 0} h(x)$
(h) $h(0)$
(i) $\lim _{x \rightarrow 2} h(x)$
(j) $h(2) \quad$
(k) $\lim _{x \rightarrow 5^{+}} h(x) \quad$
(l) $\lim _{x \rightarrow 5^{-}} h(x)$

Chapter 2: Limits
Section 3: Limits of Functions at Finite Numbers
Paul George
03:39
Biocalculus Calculus for the Life Sciences

Drug injections A patient receives a 150 -mg injection of a drug every 4 hours. The graph shows the amount $f(t)$ of the drug in the bloodstream after $t$ hours. Find
$\lim _{x \rightarrow 12^{-}} f(t) \quad$ and $\quad \lim _{x \rightarrow 12^{+}} f(t)$
and explain the significance of these one-sided limits.

Chapter 2: Limits
Section 3: Limits of Functions at Finite Numbers
Paul George
03:36
Biocalculus Calculus for the Life Sciences

$\begin{array}{ll}{\lim _{x \rightarrow 0^{-}} f(x)=2,} & {\lim _{x \rightarrow 0^{+}} f(x)=0, \quad \lim _{x \rightarrow 4^{-}} f(x)=3} \\ {\lim _{x \rightarrow 4^{+}} f(x)=0,} & {f(0)=2, \quad f(4)=1}\end{array}$

Chapter 2: Limits
Section 3: Limits of Functions at Finite Numbers
Paul George
03:53
Biocalculus Calculus for the Life Sciences

$\lim _{x \rightarrow 2 \atop x \rightarrow-\infty} f(x)=\infty, \quad \lim _{x \rightarrow-2^{+}} f(x)=\infty, \quad \lim _{x \rightarrow-2^{-}} f(x)=-\infty$
$\lim _{x \rightarrow-\infty} f(x)=0, \quad \lim _{x \rightarrow \infty} f(x)=0, \quad f(0)=0$

Chapter 2: Limits
Section 3: Limits of Functions at Finite Numbers
Paul George
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